Answer: 7
Step-by-step explanation:
The sum of a number and its reciprocal (n + [tex]\dfrac{1}{n}[/tex]) is [tex]\dfrac{50}{7}[/tex].
[tex]n+\dfrac{1}{n}=\dfrac{50}{7}\\\\\text{multiply everything by 7n to clear the denominator:}\\\\(7n)n+(7n)\dfrac{1}{n}=(7n)\dfrac{50}{7}\quad \rightarrow \quad 7n^2+7=50n\\\\\text{subtract 50n from both sides:}\qquad 7n^2-50n+7=0\\\\\text{factor the quadratic equation:}\qquad (7n-1)(n-7)=0\\\\\text{apply the Zero Product Property:}\qquad 7n-1=0\quad and\quad n-7=0\\\\\text{solve each equation:}\qquad n=\dfrac{1}{7}\quad and\quad n=7[/tex]
Since n is a natural number, the fraction is not a valid solution.
